Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2020; 57(4): 973-990

Online first article May 7, 2020      Printed July 31, 2020

https://doi.org/10.4134/BKMS.b190666

Copyright © The Korean Mathematical Society.

Harmanci injectivity of modules

Burcu Ungor

Ankara University

Abstract

For the question ``when is $E(_RR)$ a flat left $R$-module for any ring $R$?", in this paper, we deal with a class of modules partaking in the hierarchy of injective and cotorsion modules, so-called Harmanci injective modules, which turn out by the motivation of relations among the concepts of injectivity, flatness and cotorsionness. We give some characterizations and properties of this class of modules. It is shown that the class of all Harmanci injective modules is enveloping, and forms a perfect cotorsion theory with the class of modules whose character modules are Matlis injective. For the objective we pursue, we characterize when the injective envelope of a ring as a module over itself is a flat module.

Keywords: Injective module, Matlis injective module, Harmanci injective module, cotorsion module, flat module, character module, envelope

MSC numbers: Primary 16D10, 16D40, 16D50, 16E30

Stats or Metrics

Share this article on :

Related articles in BKMS

more +